Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.util.*;
// im so stupid im so stupid im so stupid
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int min = in.nextInt();
        int max = in.nextInt();
        long[] nums = new long[n];
        for( int i = 0; i < n; i++ ) nums[i] = in.nextLong();
        Arrays.sort(nums);
        boolean same = true;
        long ave = 0;
        int totalPostSame = 0;
        int postSame = 0;
        for( int i = n-1; i >= 0; i-- ) {
            // flag if not everything is the same WITHIN THE BOUNDS OF A
            if( i >= n-min ) if( nums[i] != nums[i-1] ) same = false;
            // get average, best is when using minimum amount
            if( i >= n-min ) ave += nums[i];
            // count nums that are the same as the one at A
            if( nums[i] == nums[n-min] ) {
                totalPostSame++;
                if( i >= n-min ) postSame++; // everything before A (sorted)
            }
        }
        System.out.printf("%.6f\n", (double)ave/min);

        // pascals triangle
        long[][] pascal = new long[n+1][n+1];
        for( int i = 0; i <= n; i++ ) {
            for( int j = 0; j <= i; j++ ) {
                if( i == j ) pascal[i][j] = 1;
                else if( j == 0 ) pascal[i][j] = 1;
                else pascal[i][j] = pascal[i-1][j-1] + pascal[i-1][j];
            }
        }
        // System.out.println(Arrays.deepToString(pascal));
        long total = 0;
        if( same ) {
            for( int i = min; i <= max; i++ ) total += pascal[totalPostSame][i];
        } else {
            total = pascal[totalPostSame][postSame];
        }
        System.out.println(total);
    }
}